The most common and most likely answer to this crossword clue is the 5 letter word HAIRS
I've seen this crossword clue in Independent
H
A
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R
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Buddy explains!

The straight part
We know that "Natural fibres" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case natural fibres = hairs.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does HAIRS mean?
HAIRS noun- A pigmented filament of keratin which grows from a follicle on the skin of humans and other mammals.
- The collection or mass of such growths growing from the skin of humans and animals, and forming a covering for a part of the head or for any part or the whole body.
- A slender outgrowth from the chitinous cuticle of insects, spiders, crustaceans, and other invertebrates. Such hairs are totally unlike those of vertebrates in structure, composition, and mode of growth.
- A cellular outgrowth of the epidermis, consisting of one or of several cells, whether pointed, hooked, knobbed, or stellated.
- A locking spring or other safety device in the lock of a rifle, etc., capable of being released by a slight pressure on a hair-trigger.
- Haircloth; a hair shirt.
- Any very small distance, or degree; a hairbreadth.
- Complexity; difficulty; quality of being hairy